# 3. Ensemble vs. Best Model Selection

## Introduction

In the theoretical framework of Super Learning, there are two distinct ways to utilize the cross-validated risks of your base algorithms:

1. The Ensemble Super Learner: Calculates a weighted average (convex combination) of the base learners. This “soft selection” smooths out variance, integrates different feature spaces, and generally yields the lowest finite-sample prediction error.
2. The “Best” Model Selector: Identifies the single algorithm with the lowest cross-validated risk and assigns it a weight of `1.0` (and all others `0.0`). This is a “hard selection” or “winner-take-all” approach.

While the Ensemble is asymptotically optimal, selecting the single best model is incredibly useful when interpretability is strictly tied to one specific algorithm family. Instead of manually cherry-picking the best model—which introduces researcher bias and invalidates post-selection inference—`SuperSurv` automates the selection using rigorous, internal cross-validation.

You can easily toggle between these two paradigms using the `selection` argument.

## 1. Prepare the Data

We load the `metabric` dataset and define our evaluation time grid exactly as we did in the previous tutorials.

    library(SuperSurv)
    library(survival)

    data("metabric", package = "SuperSurv")
    set.seed(42)

    # Standard Train/Test Split
    train_idx <- sample(1:nrow(metabric), 0.7 * nrow(metabric))
    train <- metabric[train_idx, ]
    test  <- metabric[-train_idx, ]

    X_tr <- train[, grep("^x", names(metabric))]
    X_te <- test[, grep("^x", names(metabric))]
    new.times <- seq(50, 200, by = 25)

    # Define a diverse library of base learners
    my_library <- c("surv.coxph", "surv.weibull", "surv.rpart")

## 2. Fit Both Super Learners

We will fit two separate `SuperSurv` models. The first will use the default Ensemble approach (`selection = "ensemble"`), and the second will use the winner-take-all approach (`selection = "best"`).

    # 1. The Ensemble Super Learner (Weighted Average)
    fit_ensemble <- SuperSurv(
      time = train$duration,
      event = train$event,
      X = X_tr,
      newdata = X_te,
      new.times = new.times,
      event.library = my_library,
      cens.library = my_library,
      control = list(saveFitLibrary = TRUE),
      verbose = FALSE,
      selection = "ensemble",     # <-- Calculates fractional weights
      nFolds = 3
    )

    # 2. The 'Best' Super Learner (Winner-Take-All)
    fit_best <- SuperSurv(
      time = train$duration,
      event = train$event,
      X = X_tr,
      newdata = X_te,
      new.times = new.times,
      event.library = my_library,
      cens.library = my_library,
      control = list(saveFitLibrary = TRUE),
      verbose = FALSE,
      selection = "best",         # <-- Selects the single best model
      nFolds = 3
    )

## 3. Inspecting the Weights

The difference between the two methodologies is immediately obvious when we inspect the meta-learner coefficients (`event.coef`).

    cat("\n--- ENSEMBLE WEIGHTS (selection = 'ensemble') ---\n")
    #>
    #> --- ENSEMBLE WEIGHTS (selection = 'ensemble') ---
    print(round(fit_ensemble$event.coef, 4))
    #>   surv.coxph_screen.all surv.weibull_screen.all   surv.rpart_screen.all
    #>                  0.5152                  0.1680                  0.3167

    cat("\n--- BEST MODEL WEIGHTS (selection = 'best') ---\n")
    #>
    #> --- BEST MODEL WEIGHTS (selection = 'best') ---
    print(round(fit_best$event.coef, 4))
    #> [1] 1 0 0

Interpretation: Notice that the Ensemble Super Learner distributes the weight across multiple models to minimize the overall loss function. The “Best” Super Learner simply looks at the cross-validated risk, identifies the champion, and gives it 100% of the weight.

## 4. Evaluate and Compare Performance

A common question in clinical research is: “Does the complexity of the Ensemble actually perform better than simply picking the best single model?”

We can answer this instantly using `eval_summary()`.

    # Evaluate the Ensemble
    cat("Performance of the ENSEMBLE Super Learner:\n")
    #> Performance of the ENSEMBLE Super Learner:
    eval_summary(fit_ensemble, newdata = X_te, time = test$duration,
                 event = test$event, eval_times = new.times)
    #>                     Model    IBS  Uno_C   iAUC
    #> 1      SuperSurv_Ensemble 0.1978 0.6569 0.6788
    #> 2   surv.coxph_screen.all 0.1989 0.6525 0.6744
    #> 3 surv.weibull_screen.all 0.1993 0.6532 0.6755
    #> 4   surv.rpart_screen.all 0.2068 0.6083 0.6541

    cat("\nPerformance of the BEST MODEL Super Learner:\n")
    #>
    #> Performance of the BEST MODEL Super Learner:
    eval_summary(fit_best, newdata = X_te, time = test$duration,
                 event = test$event, eval_times = new.times)
    #>                     Model    IBS  Uno_C   iAUC
    #> 1      SuperSurv_Ensemble 0.1989 0.6525 0.6744
    #> 2   surv.coxph_screen.all 0.1989 0.6525 0.6744
    #> 3 surv.weibull_screen.all 0.1993 0.6532 0.6755
    #> 4   surv.rpart_screen.all 0.2068 0.6083 0.6541

By comparing the resulting Brier scores and C-indices, you can empirically justify whether the “soft selection” of the ensemble is mathematically necessary for your specific dataset, or if the “hard selection” of a single model is sufficient.